Periodicity and Circle Packings of the Hyperbolic Plane
نویسنده
چکیده
We prove that given a fixed radius r, the maximum density achieved by packings of the hyperbolic plane by radius r circles is the supremum of densities of “periodic packings” (those packings with cofinite symmetry). We also show that the maximal density function is continuous as a function of radius. Our investigations lead us to consider more general questions regarding the density of periodic measures in a space of measures naturally defined for any discrete group. MSC: 52A40, 52C26, 52C23
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